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A delay-optimal caching problem in device-to-device networks with mobility is modeled. The problem arises in the context of offloading using device caching, and the offloading effect is represented by the expected network load ratio (NLR) which is the percentage of data that has to be downloaded from the network. Compared with the related studies, this letter considers minimizing delay with NLR guarantee in mobility scenarios. A lower bound of global optimum is derived, thus enabling performance benchmarking of any sub-optimal algorithm. For problem-solving, an effective search algorithm (ESA) is proposed based on the bound. Simulations are conducted to evaluate the effectiveness of the ESA algorithm.